Question

Hi, I am trying to get my head around how MLR with interactions work. Please provide:
for (a)

formula & matlab step you did to solve (if you do use statistical software)

for (b) solid justification that explains why

for (c), again good justification.

Thanks a bunch,

1.     Suppose we have a data set with five predictors, X1= GPA, X2= IQ, X3 = Gender (1 for Female and 0 for Male), X4= Interaction between GPA and IQ, and X5 = Interaction between GPA and Gender. The response variable is starting salary after graduation (in thousands of dollars). Suppose we use least squares to fit the model, and get b0 = 50, b1= 20, b2= 0.07, b3 = 35, b4 = 0.01 and b5= ⎼10.

(a) Predict the salary (in thousands of dollars) of a female with a GPA of 4.0 and an IQ of 110.

(b) Only one of the following statements is true. Say which and justify your answer briefly.

i.               For fixed values of GPA and IQ, males earn more on average than females.

ii.             For fixed values of GPA and IQ, females earn more on average than males.

iii.           For fixed values of GPA and IQ, males earn more on average than females provided that their GPA is higher than 3.5.

iv.           For fixed values of GPA and IQ, females earn more on average than males provided that their GPA is higher than 3.5.

(c) Do you agree with the following statement? Briefly justify your answer.

“Since the estimated coefficient for the GPA/IQ interaction term is very small, there is very little evidence of an interaction effect.”

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